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Terapagos's stellar form gets a buff to its base HP stat. How does this hp stat work when an already damaged Terapagos terastallizes into its stellar form? Does its hp increase based on missing hp or scales with the increased maximum hp? (How I phrased this may be unclear but I'm just asking how the increased HP stat works in battle). Please correct me if I've got how Terapagos transforms wrong, I've never actually used the turtle before.

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I think Zygarde is the only other Pokemon that can change HP mid-battle.
"the difference in HP is added to Zygarde's current HP[...]"
https://bulbapedia.bulbagarden.net/wiki/Zygarde_(Pok%C3%A9mon)#Trivia

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Same as Zygarde, or leveling up, or evolving; the new HP is always full. It retains the damage taken not the HP remaining.
Example: A max HP Terapagos has taken 50 damage (344/394 HP) after Terastallizing it will have 474/524 HP.
Basically, whenever a Pokémon's max HP increases [except when it Dynamaxes] its current HP increase by the same amount.

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Something to add to this, with Terapagos, if you somehow manage to de-terastalize it, instead of the hp staying at the same percent or being removed completely, it will actually stay at the flat value.

I noticed this while using it in the Terapagos boss fight, as i would get the heal from transforming, and then immediately be forced back out of tera, keeping all of the health restored (i only made note of it due to finding it odd that i was healing between the phases)